[tex]\displaystyle\\
Pentru~ca~49a+7b~este~un~multiplu~de~7,~iar~286~este~\mathcal{M}_7+6,~vom\\
avea~ca~c~este~\mathcal{M}_7+6,~cum~c~este~o~cifra,~vom~avea~ca~\boxed{c=6}.\\
Relatia~initiala~se~scrie,~49a+7b=280,~prin~impartire~la~7,~avem~ca\\
7a+b=40 \Longleftrightarrow 7a=40-b,~cum~b~poate~fi~cel~mult~9,~iar~40-b\\
este~un~multiplu~de~7,~vom~avea~ca~40-b=35~de~unde~\boxed{b=5}~si~\boxed{a=5}.\\
Asadar,~\boxed{a+b+c=5+5+6=\boxed{16},~\boxed{b}}.[/tex]
